Purchase any house!
Houses that can be purchased are represented by the green house icon on the ingame map.
They range in price with the cheapest being $10,000.
You can buy houses quite early on in the game, but you may not have enough money until you have completed a number of missions.
An easy way to earn enough money early in the game is to complete taxi missions; which you will need to for the "Yes I Speak English" trophy. This will net you around $30,000.

Once you have enough money, its best to save the game and then buy a property, that way you can reload your save after you have unlocked the trophy and regain your money. Houses function purely as a save point, and are thus not overly important.
The closest and easiest house to buy is south of Grove St near Emmets place. Simply walk up to the green house icon in front of the property and press (L2) to buy it.

The below video shows the exact location, as well as how to buy the house and unlock the trophy: